SOLUTION: My question is too find y: (6/p)-ax=(m/y)+k I'm not sure where to start and need a bit of help to figure out where to go with this problem. Thank you for the help

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: My question is too find y: (6/p)-ax=(m/y)+k I'm not sure where to start and need a bit of help to figure out where to go with this problem. Thank you for the help       Log On


   



Question 708042: My question is too find y: (6/p)-ax=(m/y)+k I'm not sure where to start and need a bit of help to figure out where to go with this problem.
Thank you for the help

Found 2 solutions by josgarithmetic, Edwin Parker:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Think about undoing everything that was done to y. Work from the outside inward.
(1)
Add -k to both sides.
(2)
Multiply both sides by (1/m).
See now you have some expression equals (1/y), so you really want the reciprocal of this.
(3)
Invert left and right sides and simplify the left-hand expression.

Using symmetric property of equality, we want to manage %281%2Fy%29=6%2F%28mp%29-ax%2Fm-k%2Fm.
Skipping the step, you should find y=mp%2F%286-axp-kp%29.

Answer by Edwin Parker(36) About Me  (Show Source):
You can put this solution on YOUR website!
Here's a different way that doesn't solve for the reciprocal.

6%2Fp%22%22-%22%22a%2Ax%22%22=%22%22m%2Fy%22%22%2B%22%22k 

Multiply through by LCD red%28p%2Ay%29

red%28p%2Ay%29%2Aexpr%286%2Fp%29%22%22-%22%22red%28p%2Ay%29%2Aa%2Ax%22%22=%22%22red%28p%2Ay%29%2Aexpr%28m%2Fy%29%22%22%2B%22%22red%28p%2Ay%29%2Ak

red%28cross%28p%29%2Ay%29%2Aexpr%286%2Fcross%28p%29%29%22%22-%22%22red%28p%2Ay%29%2Aa%2Ax%22%22=%22%22red%28p%2Across%28y%29%29%2Aexpr%28m%2Fcross%28y%29%29%22%22%2B%22%22red%28p%2Ay%29%2Ak

6·y - p·y·a·x = p·m + p·y·k

Get all the terms in y on the left and the term
that does not contain y on the other side:

6·y - p·y·a·x - p·y·k = p·m

Factor out y on the left:

y·(6- p·a·x-p·k) = p·m

Divide both sides by (6-p·a·x-p·k)

y%2A%286-+p%2Aa%2Ax-p%2Ak%29%2F%286-+p%2Aa%2Ax-p%2Ak%29%22%22=%22%22%28p%2Am%29%2F%286-+p%2Aa%2Ax-p%2Ak%29

y%2A%28cross%286-+p%2Aa%2Ax-p%2Ak%29%29%2F%28cross%286-+p%2Aa%2Ax-p%2Ak%29%29%22%22=%22%22%28p%2Am%29%2F%286-+p%2Aa%2Ax-p%2Ak%29

y%22%22=%22%22%28p%2Am%29%2F%286-+p%2Aa%2Ax-p%2Ak%29

Edwin